You will now use tangram shapes to explore some measurement concepts. Use the following Interactive Activity to answer Problems C1-C5.

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version of this activity, print the document (PDF) and cut out the small and medium triangles to fit into the shapes.

Using two small triangles and one medium triangle, build each of these polygons. Note 10

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Square

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Rectangle that is not a square

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Parallelogram that is not a rectangle

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Triangle

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Trapezoid

Problem C2

Without using measuring tools, can you determine which of the polygons has the greatest area? Explain. Note 11

Video SegmentWatch this video segment to see how Rosalie and Jonathan, knowing that they used the same pieces to build each shape, reasoned through the problem of whether the areas were the same.

Did you come up with any other reasons why the areas must be the same?

If you are using a VCR, you can find this segment on the session video approximately 17 minutes and 36 seconds after the Annenberg Media logo.

Problem C3

Without using measuring tools, place the polygons in order from least to greatest by the length of their perimeters. How did you determine which shape has the smallest perimeter? Note 12

Notice that the length of the hypotenuse of the small triangle and the length of the legs of the medium triangle are equal. This length can be used as one of your "nonstandard" units. What other nonstandard unit can be established by examining the lengths of the sides? Use these nonstandard units to establish the perimeters of the shapes. Close Tip

Notice that the length of the hypotenuse of the small triangle and the length of the legs of the medium triangle are equal. This length can be used as one of your "nonstandard" units. What other nonstandard unit can be established by examining the lengths of the sides? Use these nonstandard units to establish the perimeters of the shapes.

Problem C4

If we can measure without using standard units, why do we need standard units?

Video SegmentIn this video segment, Lori demonstrates the method her group used to figure out the perimeter of the five different figures, using a nonstandard unit of measure. As you watch the segment, think about the possible difficulties one may encounter when using nonstandard units of measure.

Would Lori's answer be different if she had chosen a different side or a different triangle to measure with?

If you are using a VCR, you can find this segment on the session video approximately 22 minutes and 29 seconds after the Annenberg Media logo.

Use the Pythagorean theorem to determine the lengths of the sides of the small and medium triangles. Recall that the Pythagorean theorem states that a2 + b2 = c2 for the legs (a and b) and hypotenuse (c) of a right triangle. If the length of a leg of one of the small triangles is assigned a value of 1 unit, determine the length of the hypotenuse of the small triangle and the lengths of the legs and hypotenuse of the medium triangle. Use this information to determine the perimeters of the polygons in Problem C1.